Understanding the Magic of the Bicycle

By Joseph W. Connolly, Professor of Physics/EE at the University of Scranton

Well, he tried, and helping people “understand the physical behavior of the bicycle with minimum use of mathematics” is an admirable goal, but I am afraid this misses the mark.

After chapters on “Momentum-impulse”, “Work-energy-power”, and even “Temperature and heat”, oh my, the trouble starts in chapter 10 on “Rotational motion”, specifically section 10.7 on the “Role of angular momentum in a bicycle”. Prof Connolly starts with a warning that “angular momentum is a very important physical concept,” which “is commonly misunderstood and applied in a flawed manner,” and then he immediately proceeds to misunderstand it and apply it in a flawed manner.

He continues with the example of a “simple hoop,” which “remains upright” “as long as it is rolling,” but he completely misunderstands why. Then he incorrectly asserts that the reason a rolling hoop stays upright does not apply to bicycles. The reality is that a rolling hoop stays upright because gyroscopic precession causes it to steer in the direction of a lean, just as with the front wheel of bicycles. Of course, on bicycles, gyroscopic precession is neither sufficient nor necessary for self-stability because there are other factors at play, but that doesn’t mean it doesn’t play an important role. More on that later.

The trouble continues in chapter 11 on “Torque-applications to the bicycle”. Prof Connolly employs plenty of math when he analyzes wheelies and headers, but oddly obscures the importance of center of mass location relative to the rear or front wheel by immediately using lengths instead of variables so that the relationship cannot be seen in the result. Sure, the pedal force and the coefficient of friction are also important factors, but so is the center of mass location. I suppose this oversight can be chalked up as simply an editorial choice, but the elegant result relating center of mass location to coefficient of friction was so close, it seems a shame to leave it unstated.

The main event, however, is chapter 12 on “Centripetal acceleration-turning and bicycle stability”. He does correctly point out that bicycles stay upright by steering in the direction of a lean, that a bicycle that cannot steer will not stay upright, and that many bicycle can exhibit self-stability.

Then, however, in section 12.11.1 on “Weight distribution of the handlebar-fork-front wheel” he confuses the behavior of a stationary bicycle held in some orientation by a person with the behavior of a bicycle rolling forward and not being held in some orientation. When a person holds a stationary at some lean angle, of course the front assembly will rotate about the steering axis if its center of mass is not on the axis. As an unsupported rolling bicycle leans, on the other hand, the center of mass of the rear frame and the front assembly both roll about a common axis, the line between the two tire contact patches. A crucial point that Prof Connolly misses from the two-mass-skate bike article he even cites, is that

When the TMS bicycle falls, the lower steering-mass would, on its own, fall faster than the higher frame-mass for the same reason that a short pencil balanced on end (an inverted pendulum) falls faster than a tall broomstick (a slower inverted pendulum). Because the frames are hinged together, the tendency for the front steering-assembly mass to fall faster causes steering in the fall direction.

This is a dynamic phenomenon, which can be explained in a single sentence, but a static explanation just doesn’t cut it.

It gets worse. Prof Connolly continues though to the end of chapter 12, the last chapter of the book, without ever mentioning gyroscopic effects! Oof. Sure, the two-mass-skate bike article shows that they are neither sufficient nor necessary, in theory, but it never asserts that they don’t play an important role is common bicycles. In fact, the authors state the opposite in their Supporting Online Text Material:

The benchmark bicycle entirely loses its stability if it is only changed by the removal of the wheel gyro terms.

The benchmark bicycle has no stable region when the gyro is removed.

That seems pretty clear, and this glaring omission should be the nail in the coffin of “Understanding the Magic of the Bicycle”.

That may seem harsh, and Prof Connelly, who seems like a very nice man, probably didn’t go through all the effort of writing a book just to make money, but can we say the same about the publishers, IOP Concise Physics? They are part of IOPscience, which also published the misguided “On the stability of a bicycle on rollers” in their “European Journal of Physics” that I discussed back in October 2014. It seems that they really need to find an editor that understands bikes and/or just stop publishing books and articles about them.